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Christian Enz

Publications and source records attributed to Christian Enz.

11 recordsLinked to original sources
arXiv2023

Generalized Boltzmann relations in semiconductors including band tails

Boltzmann relations are widely used in semiconductor physics to express the charge-carrier densities as a function of the Fermi level and temperature. However, these simple exponential relations only apply to sharp band edges of the conduction and valence bands. In this article, we present a generalization of the Boltzmann relations accounting for exponential band tails. To this end, the required Fermi-Dirac integral is first recast as a Gauss hypergeometric function, followed by a suitable transformation of that special function, and a zeroth-order series expansion using the hypergeometric series. This results in simple relations for the electron and hole densities that each involve two exponentials. One exponential depends on the temperature and the other one on the band-tail parameter. The proposed relations tend to the Boltzmann relations if the band-tail parameters tend to zero. This work comes timely for the modeling of classical semiconductor devices at cryogenic temperatures for large-scale quantum computing.

physics.app-ph↗
arXiv2023

Inflection Phenomenon in Cryogenic MOSFET Behavior

This brief reports the analytical modeling and measurements of the inflection in the MOSFET transfer characteristics at cryogenic temperatures. Inflection is the inward bending of the drain current versus gate voltage, which reduces the current in weak and moderate inversion at a given gate voltage compared to the drift-diffusion current. This phenomenon is explained by introducing a Gaussian distribution of localized states centered around the band edge. The localized states are attributed to disorder and interface traps. The proposed model allows to extract the density of localized states at the interface from the dc current measurements.

cond-mat.mes-hall↗
arXiv2019

Revised theoretical limit of subthreshold swing in field-effect transistors

This letter reports a temperature-dependent limit for the subthreshold swing in MOSFETs that deviates from the Boltzmann limit at deep-cryogenic temperatures. Below a critical temperature, the derived limit saturates to a value that is independent of temperature and proportional to the extent of a band tail. Since the saturation is universally observed in different types of MOSFETs (regardless of dimension or semiconductor material), the band tail is attributed to the finite periodicity of the lattice in a semiconductor volume, and to a lesser extent to additional lattice perturbations such as defects or disorder.

cond-mat.mes-hall↗
arXiv2019

Simple Thermal Noise Estimation of Switched Capacitor Circuits Based on OTAs -- Part I: Amplifiers with Capacitive Feedback

This paper presents a simple method for estimating the thermal noise voltage variance in passive and active switched-capacitor (SC) circuits using operational transconductance amplifiers (OTA). The proposed method is based on the Bode theorem for passive network which is extended to active circuits based on OTAs with capacitive feedback. It allows for a precise estimation of the thermal noise voltage variance by simple inspection of three equivalent circuits avoiding the calculation of any transfer functions nor integrals. In this Part I, the method is applied to SC amplifiers and track&hold circuits and successfully validated by means of transient noise simulations. Part II extends the application of the method to integrators and active SC filters.

eess.SP↗
arXiv2019

Simple Thermal Noise Estimation of Switched Capacitor Circuits Based on OTAs -- Part II: SC Filters

In Part I of this paper, we have shown how to calculate the thermal noise voltage variances in switched-capacitor (SC) circuits using operational transconductance amplifiers (OTAs) with capacitive feedback by using the extended Bode theorem. The method allows a precise estimation of the thermal noise voltage variances by simple circuit inspection without the calculation of any transfer functions nor integrals. While Part I focuses on SC amplifiers and track&hold circuits, Part II shows how to use the extended Bode theorem for SC filters. It validates the method on the basic integrator and then on a first-order low-pass filter by comparing the analytical results to transient noise simulations showing an excellent match.

eess.SP↗
arXiv2019

Cryogenic MOSFET Threshold Voltage Model

This paper presents a physics-based model for the threshold voltage in bulk MOSFETs valid from room down to cryogenic temperature (4.2 K). The proposed model is derived from Poisson's equation including bandgap widening, intrinsic carrier-density scaling, and incomplete ionization. We demonstrate that accounting for incomplete ionization in the expression of the threshold voltage is critical for an accurate estimation of the current. The model is validated with our experimental results from nMOSFETs of a 28-nm CMOS process. The developed model is a key element for a cryo-CMOS compact model and can serve as a guide to optimize processes for high-performance cryo-computing and ultra-low-power quantum computing.

physics.app-ph↗
arXiv2018

Characterization and Modeling of 28-nm FDSOI CMOS Technology down to Cryogenic Temperatures

This paper presents an extensive characterization and modeling of a commercial 28-nm FDSOI CMOS process operating down to cryogenic temperatures. The important cryogenic phenomena influencing this technology are discussed. The low-temperature transfer characteristics including body-biasing are modeled over a wide temperature range (room temperature down to 4.2\,K) using the design-oriented simplified-EKV model. The trends of the free-carrier mobilities versus temperature in long and short-narrow devices are extracted from dc measurements down to 1.4\,K and 4.2\,K respectively, using a recently-proposed method based on the output conductance. A cryogenic-temperature-induced mobility degradation is observed on long pMOS, leading to a maximum hole mobility around 77\,K. This work sets the stage for preparing industrial design kits with physics-based cryogenic compact models, a prerequisite for the successful co-integration of FDSOI CMOS circuits with silicon qubits operating at deep-cryogenic temperatures.

cond-mat.mes-hall↗
arXiv2018

Design-oriented Modeling of 28 nm FDSOI CMOS Technology down to 4.2 K for Quantum Computing

In this paper a commercial 28-nm FDSOI CMOS technology is characterized and modeled from room temperature down to 4.2 K. Here we explain the influence of incomplete ionization and interface traps on this technology starting from the fundamental device physics. We then illustrate how these phenomena can be accounted for in circuit device-models. We find that the design-oriented simplified EKV model can accurately predict the impact of the temperature reduction on the transfer characteristics, back-gate sensitivity, and transconductance efficiency. The presented results aim at extending industry-standard compact models to cryogenic temperatures for the design of cryo- CMOS circuits implemented in a 28 nm FDSOI technology.

physics.app-ph↗
arXiv2018

Cryogenic MOS Transistor Model

This paper presents a physics-based analytical model for the MOS transistor operating continuously from room temperature down to liquid-helium temperature (4.2 K) from depletion to strong inversion and in the linear and saturation regimes. The model is developed relying on the 1D Poisson equation and the drift-diffusion transport mechanism. The validity of the Maxwell-Boltzmann approximation is demonstrated in the limit to zero Kelvin as a result of dopant freeze-out in cryogenic equilibrium. Explicit MOS transistor expressions are then derived including incomplete dopant-ionization, bandgap widening, mobility reduction, and interface charge traps. The temperature dependency of the interface-trapping process explains the discrepancy between the measured value of the subthreshold swing and the thermal limit at deep-cryogenic temperatures. The accuracy of the developed model is validated by experimental results on a commercially available 28-nm bulk CMOS process. The proposed model provides the core expressions for the development of physically-accurate compact models dedicated to low-temperature CMOS circuit simulation.

cond-mat.mes-hall↗
arXiv2018

Cryogenic Characterization of 28 nm Bulk CMOS Technology for Quantum Computing

This paper presents the first experimental investigation and physical discussion of the cryogenic behavior of a commercial 28 nm bulk CMOS technology. Here we extract the fundamental physical parameters of this technology at 300, 77 and 4.2 K based on DC measurement results. The extracted values are then used to demonstrate the impact of cryogenic temperatures on the essential analog design parameters. We find that the simplified charge-based EKV model can accurately predict the cryogenic behavior. This represents a main step towards the design of analog/RF circuits integrated in an advanced bulk CMOS process and operating at cryogenic temperature for quantum computing control systems.

cond-mat.mes-hall↗